Native Oxidation and Complex Magnetic Anisotropy‐Dominated Soft Magnetic CoCrFeNi‐Based High‐Entropy Alloy Thin Films

Abstract Soft magnetic high‐entropy alloy thin films (HEATFs) exhibit remarkable freedom of material‐structure design and physical‐property tailoring, as well as, high cut‐off frequencies and outstanding electrical resistivities, making them potential candidates for high‐frequency magnetic devices. In this study, a CoCrFeNi film with excellent soft magnetic properties is developed by forming a novel core–shell structure via native oxidation, with ferromagnetic elements Fe, Co, and Ni as the core and the Cr oxide as the shell layer. The core–shell structure enables a high saturation magnetization, enhances the electrical resistivity, and thus reduces the eddy‐current loss. For further optimizing the soft magnetic properties, O is deliberately introduced into the HEATFs, and the O‐incorporated HEATFs exhibit an electrical resistivity of 237 µΩ·cm, a saturation magnetization of 535 emu cm−3, and a coercivity of 23 A m−1. The factors that determine the ferromagnetism and coercivity of the CoCrFeNi‐based HEATFs are examined in detail by evaluating the microstructures, magnetic domains, chemical valency, and 3D microscopic compositional distributions of the prepared films. These results are anticipated to provide insights into the magnetic behaviors of soft magnetic HEATFs, as well as aid in the construction of a promising material‐design strategy for these unique materials.

. Microstructures of the CoCrFeNi thin film: the bright-field in-plane TEM morphology of CoCrFeNi thin film (a) and the (a 1 )corresponding SAED pattern (b), the HRTEM images, the corresponding FFT spectra and filtered images of the FCC(b 1 ) and BCC(b 2 ) structures in the CoCrFeNi thin film. Figure S3. Microstructures of the Al 0.5 CoCrFeNi films: the bright-field in-plane TEM morphology (a) and the corresponding SAED pattern (a 1 ) The HRTEM images(b), the corresponding FFT spectra and filtered images of the FCC(b 1 ) and BCC(b 2 ) structures. Figure S4. The grain sizes of the films: the grains in the CoCrFeNi thick film (a) the small grains in the CoCrFeNi thin film (b) the large grains in the CoCrFeNi thin film (c) (there are very few large grains, the statistical size value of large grains only accounted for 1/10 of the total grains statistical size value).

Figure S5
. XRD fits patterns of the diffraction peak the as-deposited HEA films (red and green dash lines correlate to the diffraction peak of FCC and BCC, blue solid line is the sum of the fitting curves).

The content of the BCC phase
The α phase volume fraction ( v  ) is related to the diffracted intensity of the X-ray beam on the {HKL} plane, (   HKL I  ), as follows: [1]   where K is the constant for a measurement, R  can be given by the following formula: [1]       where   HKL P  is the multiplicity factor, The present work, the relationship between the volume fractions of BCC and FCC phases in Al x CoCrFeNi (x = 0 ~ 0.5) film is described as follows: Here, selecting {111} FCC and {110} BCC calculates the volume fraction. The amplitude squared of the structure factor (   f , respectively, where f is the the atomic scattering factor for the FCC and BCC phases, which is closely related to the atomic number z. [1] The chemical disorder of high entropy films can ensure that the components doesn't fluctuate significantly in the FCC and BCC phases. Therefore, the effective atomic number of the two phases, Z eff , are basically same. [2,3] Based on this feature, f is basically consistent in the two phases. Table S1 shows the values of phase fractions and other parameters used for calculations.

Fitting Section
In soft magnetic materials, the area of the ring surrounded by the hysteresis loop is quite small, that is, the rising and falling stages of the curve are very close. We assume that each H value corresponds to only one M(H) value, so the M value in the magnetization curve can be obtained by the average value of M in the rising and falling stages of the hysteresis loop, as shown in the following equation: [4] avg = 2 Where, M u and M e represent the magnetization of the upper and lower parts of the hysteresis loop in the first quadrant respectively, and it is assumed that they pass through the origin.
To obtain the effective anisotropy constant more accurately, it is often necessary to fit the magnetization curve to determine the in-plane magnetization direction and the integral area difference between the in-plane magnetization direction and the vertical axis. Therefore, in order to obtain better fitting effect, as shown in the following equation: The exponential term of this formula can produce a good fitting effect on the magnetization curve. By adding the two exponential terms, the fitting scope is wider and all our curve fitting parameters can be better fitted as follows: